Question

Three consecutive even numbers have a sum where one half of that sum is between 90 and 105

Answer 1

$2n;\ 2n+2;\ 2n+4-three\ consecutive\ even\ numbers\\\\90 \ \textless \ \dfrac{1}{2}(2n+2n+2+2n+4) \ \textless \ 105\\\\90 \ \textless \ \dfrac{1}{2}(6n+6) \ \textless \ 105\\\\90 \ \textless \ 3n+3 \ \textless \ 105\ \ \ |divide\ both\ sides\ by\ 3\\\\30 \ \textless \ n+1 \ \textless \ 35\ \ \ |subtract\ 1\ from\ both\ sides\\\\29 \ \textless \ n \ \textless \ 34\to n\in\{30;\ 31;\ 32;\ 33\}\\\\Answer:\\60;\ 62;\ 64\ or\ 62;\ 64;\ 66\ or\ 64;\ 66;\ 68\ or\ 66;\ 68;\ 70.$